Question

Part III: The following question requires hand calculations. Be sure to show ALL work and round final answers appropriately. You MUST show all work in order to receive full points.

Z-scores (20 points total)

The average age reported for onset into delinquent activity for the population of prison inmates is 12 with a standard deviation of 2.4. Based on this information and assuming the population is normally distributed:

Z=(X-µ)/s

An inmate's age of one set is 17. Is he in the top 15% of ages? (5 points)

Answer 1

Solution,

Given that,

mean = = 12

standard deviation = = 2.4

n = 17

= = 12

= / n = 2.4 / 17 = 0.58

Using standard normal table,

P(Z > z) = 15%

= 1 - P(Z < z) = 0.15  

= P(Z < z ) = 1 - 0.15

= P(Z < z ) = 0.85

= P(Z < 1.036) = 0.85  

z = 1.036

Using z-score formula  

= z * +

= 1.036 * 0.58 + 12

= 12.6